A Mathematical study about the "Coherence Set" in Polarimetric Interferometry

Abstract:
One of the key idea of PolInSAR data is that it is possible to obtain interferometric coherence from all possible linear combinations of polarization states. These linear combinations are described by two vectors called two generic mechanisms: one for each image of the pair. In a first part, this paper presents a mathematical study about the representation of the coherence shape in the complex plane, that means the set of possible coherences defined using the same complex unitary vector for both antennas. This definition of the coherence set constrained to a unique mechanism is well adapted in case of an interferometric configuration where both antennas as well as the incidence angles are very close. In a second part of the paper, a generalization of the representation of the coherence set defined using two different mechanisms is investigated. Using different vectors makes it possible to take into account polarimetric decorrelation between the two scattering mechanisms. This can be useful in case of temporal decorrelation or for larger baselines. In this case, the location of the generalized coherence is a disk in the complex plane, and cannot be used to deduce information about the interferometric angles. Therefore, it is necessary to introduce another constraint between both mechanisms.